Yes, it's quite safe, pick a reputable tour company - there are a few out there - I used SoloEast, and wouldn't hesitate to recommend them.
I'd advise against going alone, as you'll probably find it a bit boring, there were a variety of different nationals on our tour, and not too many were terribly chatty, and it's a long day.
Kiev, where you'll most likely stay was fine, and incredibly cheap! we didn't encounter any trouble, other than the usual beggars, but then we were 3 strapping lads - We stayed at KievInn, just up the hill from Independence Square, and abut 1 min's walk from the tour departure spot.
Id recommend it to anyone, hands-down one of the best places I've been.